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The Economics of the Right to be Forgotten∗
Byung-Cheol Kim† Jin Yeub Kim‡
March 16, 2015
Abstract
We examine the underlying economics behind the emerging issue of the so-called “right to
be forgotten,” which subsumes the right for individuals to ask for ‘inadequate, irrelevant
or no longer relevant, or excessive’ information about them to be dropped from Internet
searches. At stake is the conflict between the privacy right and other fundamental rights
such as the freedom of speech, expression, and access to information. First, we analyze
a legal dispute game between a petitioner, claiming the right to be forgotten, and an
Internet search engine. In particular, we characterize conditions under which litigation
arises as an equilibrium outcome. Then we provide comparative static results on the
probability of lawsuits and the likelihood of broken-links, in connection to the social
value of information. Our model offers a useful framework in understanding the effects
of Europe’s expansion of the right to be forgotten to non-European websites: If the
European ruling applies to all global search engine domains, then the expected amount
of broken-links would fall.
Keywords: Right to be forgotten, privacy, litigation, internet services.
JEL Classification: C72, D82, K20, K41, L86.
∗First version: December 2014. This is a preliminary version. Any comment will be appreciated. We thankJay Pil Choi and Lars Stole for helpful feedback.†Department of Economics, Georgia Institute of Technology. E-mail: byung-cheol.kim@econ.gatech.edu,
Webpage: https://sites.google.com/site/byungcheolkim76‡Department of Economics, University of Nebraska-Lincoln. E-mail: shiningjin@gmail.com, Webpage:
https://sites.google.com/site/jinyeubkim
Kim & Kim: The Right to be Forgotten
1 Introduction
In 2009, Mario Costeja Gonzalez, a Spaniard lawyer, requested Google Spain the removal
of a link to a digitized 1998 article in La Vanguardia newspaper about the forced sale of
properties arising from social security debts – one of which belonged to Costeja. His grounds
were that the forced sale had been concluded years before, a debt had been paid in full, and
information regarding his home-foreclosure notices was no longer relevant but defamatory.
When the request was unsuccessful, Costeja sued Google, the dominant search engine that
covers more than 90 percent of all online searches in Europe. The case was eventually elevated
to the European Court of Justice (ECJ). In May 2014, the court found for Costeja that both
Google Inc. and its subsidiary Google Spain were required to remove the list of pertinent
links from Google search results on Costeja’s name. More generally, the court ruled that the
operator of a search engine is obliged to remove, when requested by an individual, links to
web pages that contain ‘inadequate, irrelevant or no longer relevant, or excessive’ information
relating to that person in the results page following a search on the data subject’s name, where
the interests in those results appearing are outweighed by the person’s privacy rights.1
Upon the ruling Google launched the online request process, and has complied with
roughly 41 percent of more than 231,000 link-removal requests that it has received over the
last ten months from individuals in EU and EFTA countries. Table 1 shows data on total
number of requests Google has received, total number of URLs that Google has reviewed for
removal, and the percentages of URLs removed for the top five countries as of March 15,
2015 since the launch of Google’s official request process on May 29, 2014. Table 2 lists the
ten domains where Google removed the most URLs from search results. Not surprisingly,
Facebook.com tops among the most impacted domains, a majority of which offer search or
social networking services.
The European ruling on the Costeja case and the subsequent compliance of Google set
a major precedent over what is so-called the “right to be forgotten,” the notion of which is
derived from numerous preexisting European ideals on private information about individuals.
The right to be forgotten essentially allows individuals to have information about themselves
1Case C-131/12 Google Spain SL, Google Inc. v Agencia Espanola de Proteccion de Datos, Mario CostejaGonzalez [2014] ECLI:EU:C:2014:317.
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Table 1: European privacy requests for search removals on Google
Country Total requests Total URLs evaluated % URLs removed
All EU and EFTA 231,358 836,142 40.6France 47,154 157,560 47.8
Germany 38,801 147,144 49.0U.K. 29,409 114,875 35.5
Spain 21,436 69,555 35.7Italy 17,369 59,551 26.5
Source: https://www.google.com/transparencyreport/removals/europeprivacy/
(updated as of Mar. 15, 2015, 6 pm)
Table 2: Most impacted sites by Google’s removal of links
Web domain Total URLs requested for removal Type
facebook.com 5,522 social networking serviceprofileengine.com 5,221 social network searchgroups.google.com 3,702 discussion groups
youtube.com 3,384 video-sharingbadoo.com 3,307 dating-focused social networking
yasni.de 2,298 search enginewhereevent.com 2,267 event search tool
192.com 2,151 online directoryplus.google.com 2,150 social networking service
yasni.fr 1,900 search engine
Source: The same with Table 1; type is added by authors. (updated as of Feb. 15, 2015)
deleted so that they cannot be found by search engines.2 The application scope of such
right remains a controversial topic and the consensus is not yet made. The key source of
controversy stems from different views on the right to be forgotten and related fundamental
rights between European and American legal frameworks.3 Nonetheless, as the European
ruling legally solidified the right to be forgotten as a fundamental human right, the already-
issued EU guidelines surrounding data protection calls on Google to apply the European
ruling to all of its global search engine domains and not only to its European local domains.
This precipitated a spark debate on the global extension of the scope of the European ruling
2In fact, the right to be forgotten is more broadly applicable to any Internet service provider not onlylimited to search engines. However because the most notable and majority of cases regard Google’s searchresults, we will focus on “Google” as a representative player in subsequent discussions of this paper.
3We offer a brief literature review on opposed approaches to the right to be forgotten between Europe andU.S. in Subsection 1.1.
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and the establishment of the right to be forgotten to the status of an internationally accepted
human right.
At the heart of the debate lie several conflicting interests. The individuals can rightly
desire to avoid any harm incurred by the search result links that are defamatory, embarrassing,
or misleading. Therefore, the individuals’ rights to de-list the prominence of such information
in search engine results are indispensable on the basis of privacy rights. But what about the
rights of the individuals seeking information or of the search engines providing information?
Network users are deprived of the links that help them easily find contents, and search
engines may experience profit loss from broken links. In essence, the removal of links under
the pretext of protecting privacy rights can encroach other fundamental rights, such as the
freedom of speech, expression, and access to information, and generate various layers of social
costs.
Then what is the proper balance between clashing values of privacy and free speech, or
the right to be forgotten versus the right to remember? Various attempts have been made
to discuss these issues, much of which take legal or philosophical perspectives. However, to
the best of our knowledge, any formal analysis on the underlying economics has hardly been
conducted. How would the value of the right to be forgotten relative to the right to remember
influence individuals’ behavior and search engines’ response? Does the number of requests
for removal that are processed exceed the socially optimum amount? Are there too many or
too few links taken down from a social welfare perspective? In an attempt to answer these
questions, we build a game-theoretical model to provide the economics of the right to be
forgotten. Our goal in this paper is to offer not only theoretical insights but also practical
implications on the related issues.
In Section 2, we present a model of the right to be forgotten as an extensive-form legal
dispute game between a petitioner and a web search engine (Google). The petitioner, who
suffers harm from the links, can claim the removal of related links; the claiming is a costly
process. The search engine can either accept the claim or reject it depending on its profit
loss, which is positively related with network users’ loss that arises when the links are broken.
If the claim is rejected, then the petitioner can proceed to court against the search engine,
where litigation is costly for both parties. The petitioner’s uncertainty about the search
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engine’s loss from the broken links plays a key role in our model because the search engine,
with private information, can make a better assessment of the trial’s expected outcome.
In Section 3, we characterize conditions under which litigation may arise as an equilibrium
outcome. Given the associated primitives, we obtain a unique sequential equilibrium in the
legal dispute game. In particular, as long as the claim fee is sufficiently small, the petitioner
will act aggressively and always claim his right to be forgotten, in hopes of his claim being
accepted and, despite rejection, of winning in a trial. Upon rejection, litigation always ensues
if the petitioner’s harm is fairly large; otherwise litigation still takes place with positive
probability. Therefore, regardless of the size of the petitioner’s harm, there is always the
possibility of lawsuits as the equilibrium outcome, which leads to broken links.
We give the comparative static results regarding the probability of lawsuits and the like-
lihood of broken-links in Section 4. As a standard intuition might suggest, if network users’
loss from broken links (S) is higher, then more types of Google reject the petitioner’s claim
and the petitioner correctly expects to win a trial less often. Surprisingly, the petitioner can
still commit to litigate with probability one when rejected (for up to a sufficiently large size
of S), and thus more number of cases are brought to court. Even so, less types of Google
accepting the claim primarily affects the likelihood of broken-links as a resulting equilibrium
outcome to fall unambiguously. The intuition is as follows: The probability of Google’s rejec-
tion increases as S increases, raising the probability of lawsuits; however the petitioner has
no certainty of winning in court,4 and thus the effect of the increased probability of Google’s
rejection is second order.
Our equilibrium and comparative static results provide two interesting implications as is
discussed in Section 5. First, informational asymmetry influences the petitioner’s assessment
of the trial’s expected outcome; and thus our model predicts that the expected number of
broken links exceeds the socially optimum amount if the petitioner overestimates his winning
probability, and the converse is true if the petitioner underestimates. Second, even if the
individual’s harm from the links is relatively small compared to total social welfare lost by
the broken links,5 the petitioner’s lower expected probability of winning in court does not
4In fact, the petitioner’s expected probability of winning in court declines as S increases.5In Section 5, we define the value of the right to be forgotten to be the (ex-post) social welfare loss from
the links, measured by the petitioner’s harm; and the value of the right to remember to be the (ex-post) socialwelfare loss from the broken links, measured by network uses’ and search engine’s loss. For our purpose, the
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deter him from acting aggressively. Hence, an excessive amount of claims are brought to
court and resolved by costly court-imposed judgments. Thus we confirm as an equilibrium
phenomenon one conspicuous concern in the debate of the right to be forgotten: Too many
requests for the removal of links are processed from a social welfare perspective.
In Section 6, we relate our equilibrium results to the current situation regarding the
European ruling and the debate on its expansion. In particular, we give a numerical example
to explain the economics behind the European ruling and Google’s compliance; and discuss
how our results offer a reasonable prediction of individuals behavior of claiming the RTBF
and Google’s response in removing the links if the European ruling expands to all of Google’s
global search engine domains. Interestingly, if Google applies the European ruling to non-
European websites as well, then the amount of broken-links would decrease because Google
will then decline the removal requests much more often. Therefore, our key finding may
invalidate the ground for concerns about the threatening impact of the expansion on the
right to freedom of speech.
Several possible extensions arise in our model that require some discussion; we mention a
few in Section 7. First, as a complement to Section 4, we give comparative static results with
respect to changes in litigation costs. Second, the modeling framework we developed here
could be equally applicable under the British rule on litigation fees. Also suitable versions
of the results continue to hold when uncertainty is two-sided. We could also relax or impose
correlation between the players’ losses, but the logic of our analysis suggests that the main
insights of the results in this paper would also apply to this extension but with some added
nuances. Lastly, we address how the right to be forgotten affects behavior of professionals
who have reputational concerns. All proofs for the results in the main text can be found in
Appendix A.
1.1 Literature Review
Before closing the introduction, we offer a brief review on the burgeoning literature on the
right to be forgotten. Many legal scholars focus on describing institutional and conceptual
differences in how Europeans and Americans have approached to the problem (e.g., Ambrose
definition of the right to remember subsumes both the right of free speech and access to information and thesearch engine’s right to do business.
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and Ausloos (2013); Bennett (2012); Bernal (2014); McNealy (2012); Rosen (2012a,b); and
Walker (2012)). For example, Rosen (2012b) addresses the differences between European
and American conceptions of the balance between privacy and free speech and how the
right to be forgotten represents a threat to free speech. He notes that in Europe the right
to be forgotten finds its intellectual root in the right to be oblivion, le droit a l’oubli in
French law: a convicted criminal has a right to oppose the publication of his or her criminal
history upon serving time; whereas in America such right would make a direct conflict to the
First Amendment to the United States Constitution, which protects the freedom of speech.6
McNealy (2012) indicates that while some plaintiffs in the U.S. have attempted to assert a
right to be forgotten through the privacy law of the U.S., the U.S. court has seldom allowed
for removing certain information from the press. Instead the court recognized the “right to
be alone,” which grants a recovery to an injured party from the public disclosure of private
information under the tort of “invasion of privacy.”7
Another strand of literature elaborate on web technological solutions in implementing a
right to be forgotten. This is important because any practical enforcement and implemen-
tation of the right to be forgotten must be assisted and bounded by technological solutions.
According to Rosen (2012a), there is a blob machine-like solution such as X-Pire and Tiger-
Text, which allows individual users to put expiration dates on text messages or photos that
are copied and reposted by others. O’Hara (2012) discusses technological solutions available
to data controllers, like Facebook or Google. Under the current European regulation, the
right to be forgotten applies to the takedown of the reposted content without delay. For
example, Facebook is forced to delete the reposted pictures when the original owner demands
the erasure; but it takes proper tech-solutions to trace, identify, and delete all relevant data.
The blob machine-like solution may provide the initial owners with an immediate technolog-
ical solution. While we abstract away from technological aspects in the enforcement of the
6This stark contrast stands out in the following case in point. Two Germans murdered a famous Germanactor Walter Sedlmayr and they served their time. Released from prison, they attempted to delete their namesfrom the German Wikipedia article of the late Mr. Sedlmayr, which successfully led to the deletion. Theyfurther moved to scrub their names from the English-language version of the Wikipedia article by filing asuit against the Wikimedia Foundation, the non-profit American organization (located in San Francisco) thatruns Wikipedia. However, the Foundation did not comply with the request obviously relying on the FirstAmendment; their names are still posted. See John Schwartz, Two German Killers Demanding AnonymitySue Wikipedia’s Parent, N.Y. TIMES, Nov. 12.2009.
7See Purtz v. Srinvisan, No. 10CESC02211 (Fresno Co. Small Cl. Ct. Jan. 11, 2011) in McNealy (2012).
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right to be forgotten, our model does not rule out the interpretation that the court’s decision
rule (for a practical enforcement) might be bounded by available technologies.
The contribution of our paper is that we offer a first formal model of the economics behind
the right to be forgotten. We conclude the introduction by noting that the methodological
approaches in the literature on the economic analysis of litigation is somewhat similar to that
in the current paper. For example, in his seminal paper, Bebchuk (1984) models an extensive
form game of two parties’ litigation and settlement decisions, in which the defendant has
private information about his liability. The key difference is that Bebchuk (1984) shows how
informational asymmetry influences the optimal settlement amount in pretrial negotiation;
whereas we focus on the relative values of various social welfare loss and their effects on the
probability of lawsuits and broken-links as equilibrium outcomes.
2 The Model
Two risk-neutral parties are involved in a potential legal conflict regarding the right to be
forgotten – the RTBF game. A petitioner, denoted as P, alleges that he suffers harm of size
h > 0 from the links provided on a web search engine, say Google, denoted as G.8 Google
loses L ≥ 0 if the links are removed. At the heart of the debates on the right to be forgotten
lies one important issue that cannot be overlooked: the effect of the broken links not only on
Google but also on the general public – in particular, network users. For example, some users
may need to exert more effort (or may even fail) to find the right content without the links
offered by the search engine. To capture such externality, we denote by S ≥ 0 any welfare,
generally construed, that is lost if the links are broken. This parameter can be interpreted
as the value of searched information to network users, or more broadly as the social value of
the freedom of speech.
We assume that Google internalizes users’ welfare loss as her own profit loss, and thus
impose a direct relationship between L and S.9 In particular, let L = γS, where γ ∈ [0, γ]
8For exposition, we use male pronouns for the petitioner and female pronouns for Google.9This assumption substantially simplifies the exposition while conveying all the key insights of our model.
Suitable versions of the results continue to hold when this assumption is relaxed as long as L is privateinformation to Google. But it seems natural to impose a linear relationship between L and S; for example, thebroken links can lower advertising profits from users’ search. In contrast, we do not impose any deterministicrelationship between h and S (nor h and L). We discuss correlation between losses in Subsection 7.4.
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measures the fraction of users’ welfare loss for which Google will internalize, possibly greater
than one. The petitioner’s harm and users’ welfare loss are common and public knowledge,
whereas only Google knows her true γ.10 The petitioner believes that γ is drawn from a
non-degenerate distribution F (·) over the interval [0, γ].
Figure 1: The game tree
The game tree illustrated in Figure 1 describes the sequence of events. The petitioner
first chooses either to “claim” (i.e., requests Google to remove the links) at a fee of c > 0, or
to make “no claim.” This decision is made without knowing Google’s γ.11 Once a claim is
filed, Google then decides whether to accept or reject the claim. If Google accepts and takes
down the links, she loses γS and the petitioner receives payoff of −c. If Google rejects, then
the petitioner will have to choose whether to “litigate” or “give up” (i.e., drop the case),
still not knowing Google’s γ. By giving up, the petitioner’s payoff is −h − c and Google’s
payoff is zero. If the petitioner litigates and a trial takes place, then the litigation costs of
the petitioner and Google will be CP and CG, respectively. Let β be the likelihood of the
petitioner’s prevailing in a trial. Under the American rule on litigation fees, the expected
payoffs from litigation then are −(1 − β)h − c − CP for the petitioner and −βγS − CG for
10We can extend our model with two-sided incomplete information, which will be briefly discussed in Sub-section 7.3.
11If γ is known to the petitioner, then the petitioner knows exactly when Google will accept or reject hisclaim. If Google is expected to reject the claim, then the claim itself incurs a mere cost with no additionalexpected benefit. Therefore, there is no reason for the petitioner to claim at a certain fee prior to litigationwhen he is sure of rejection under complete information.
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Google.12
The expected outcome of a trial depends on the factual issues relevant to the links in
question; and so the expected ruling of a trial can be estimated by h, γ, and S. Thus it will
be assumed that β = g(h, γ, S), where g is a twice-differentiable function, 0 ≤ g(h, γ, S) ≤ 1,
and its partial derivatives satisfy gh ≥ 0, gγ ≤ 0, and gS ≤ 0 for all (h, γ, S). The conditions on
the first derivatives assume that the probability that the court rules in favor of the petitioner
increases if the net social welfare saved by taking down the links (h) increases, and decreases
if the net social welfare saved by not taking down the links (γS + S) increases (by either a
higher γ or S).13 Note that Google possesses some private information that is relevant to
estimating the trial’s expected outcome. Google’s private information allows her to make a
better assessment of the likelihood of the petitioner’s prevailing in a trial (to be g(h, γ, S));
while the petitioner does not know γ, and correspondingly g(h, γ, S), but would form a
posterior expectation of the winning probability g(h, γ, S) given F (·). We further assume
that gγγγ + 2gγ < 0 and g + gγγ < 1, ∀γ ∈ [0, γ]. The first condition imposes upward
concavity on Google’s expected payoff from litigation, ensuring that G’s best responses are
well defined; the second condition requires that G’s marginal loss from rejecting relative to
accepting with respect to γ is less than 1, which is essentially the same thing as imposing
strict monotonicity of G’s best responses.14
3 Equilibrium Results
In this section, we characterize conditions under which court-imposed settlements (or law-
suits) may arise as an equilibrium outcome, and analyze equilibria of this game. Our model
does not convey any substantial insight if all types of Google always accept the claim or if the
petitioner always gives up upon rejection. For our model to capture many situations in which
12We briefly examine our model under the British rule of litigation fees and discuss relevant results inSubsection 7.2.
13Note that if the petitioner wins the trial, then the links are removed and the ex-post social welfare loss isγS+S; whereas if Google wins, then the links remain and the ex-post social welfare loss is h. As an example,we can assume g(h, γ, S) = h
h+γS+S. Although such functional form may seem ad-hoc, it summarizes the
essential component of the court’s decision rule that depends on the relative balance between social welfareand loss that arise when one party wins.
14The second assumption is essential for keeping the analysis tractable, but might also be viewed as ensuringthat the marginal value of switching from accepting to rejecting is monotone increasing in G’s type γ, orrequiring a strictly increasing differences property on G’s expected payoffs.
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the court judgment plays a role in the issue of RTBF and to yield a rich set of theoretical
implications, we rule out such cases with Assumptions 1 and 2 given in the text.
Let the petitioner’s strategy be represented by (p1, p2), where p1 denote the probability
that the petitioner would claim and p2 denote the conditional probability that he litigates
if Google rejected. Let us first consider the outcome after the path of play reached the
decision node controlled by Google, i.e., p1 = 1. In this continuation subgame, Google with
type γ compares her payoff from accepting, −γS, with her expected payoff from rejecting,
(1− p2) · 0 + p2 [−g(h, γ, S)γS − CG], when she anticipated that the petitioner would behave
according to p2. Google with type γ is just indifferent between accepting and rejecting the
claim if she believes that the probability of P’s litigation is p2 if and only if:
γS = p2 [g(h, γ, S)γS + CG] . (3.1)
Lemma 1. There exists a unique γ > 0 that satisfies (3.1) given p2 > 0.
Define γG be such unique value of γ that satisfies (3.1). We assume that dg(h,γG,S)dh > 0
and dg(h,γG,S)dS < 0.15 Note that given p2 > 0, it will not be the case that Google will always
reject no matter what her type is.
Because G’s expected payoffs satisfy the strictly increasing differences property, i.e., the
difference between her expected payoff from rejecting and her payoff from accepting is a
strictly increasing function of her type γ, no matter what P’s action may be, G’s higher
types find rejection relatively more attractive than lower types do. Thus Google will always
want to use a cutoff strategy.
Lemma 2. Google’s best response against any strategy of the petitioner, p2, is using a cutoff
strategy with the cutoff γG that satisfies (3.1), characterized as:
(i) all types with γ ≥ γG will reject the claim; and
(ii) all types with γ < γG will accept the claim.
Now at the petitioner’s node after the claim has been rejected, P compares his payoff
15Note that ∂γG∂p2
> 0, ∂γG∂h
> 0, ∂γG∂S
< 0, and ∂γG∂CG
> 0.
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from giving up, −h− c, with his expected payoff from litigation,
− (1− g(h, γ(γG), S)S + S)h− c− CP , (3.2)
where γ(γG) ≡ E[γ|γ ≥ γG] is P’s posterior expectation of γ if the claim is rejected, given by
E [γ|γ ≥ γG] =
∫ γ
γG
xf(x)
1− F (γG)dx. (3.3)
If F (·) is a Uniform distribution over the interval [0, γ], then (3.3) becomes γG+γ2 . It is easy
to see that this is a monotonically increasing function of γG. In fact it is true for any generic
distribution F as long as it is non-atomic over the interval [0, γ], where γ need not equal
one.16 Therefore as more types accept (i.e., γG increases), their expected γ increases, in
turn lowering the petitioner’s expected probability of winning in court, and so the term (3.2)
monotonically falls with γG.
Suppose now that all types of G reject the claim. Then γG = 0, and the posterior
expectation of γ equals the priors. If P’s expected payoff from litigation were already less than
his payoff from giving up under the priors, then as more types accept, litigation would become
even less profitable; in such cases, the petitioner will always give up upon rejection regardless
of his posterior expectations. The following assumption rules this out by requiring that the
petitioner’s case has merit – P’s expected payoff from litigation is greater than his payoff
from giving up given the prior distribution of Google’s types,17 i.e., − (1− g(h,E(γ), S))h−
c− CP > −h− c.
Assumption 1. g(h,E(γ), S)h > CP .
Assumption 1 requires that the petitioner’s harm should not be too small, nor its litigation
cost should be too large; or the social value of the freedom of speech, captured by S, should
not be too large in order for litigation to be ex-ante profitable to the petitioner. Now under
16This is intuitive because when more types reject, the interval of types who reject increases (i.e., γG falls),and their expected γ decreases.
17Bebchuk (1984) assumes that litigation has a positive expected value for the plaintiff even if the defendantis of the lowest type. Translating into our model, this assumption is equivalent as to assume that litigation isprofitable against Google of the highest type γ. In other words, there is some minimal probability of P winningin litigation and that litigation is profitable even with this minimal probability. In this sense, Assumption 1is a weaker version of Bebchuk (1984)’s assumption.
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Assumption 1, even if all types of Google reject the claim, litigation would be profitable to
the petitioner compared to giving up.
In addition, it is of no interest if all types of Google were to always accept the claim. This
happens when γG ≥ γ. The sufficient condition in Lemma 3 ensures that γG < γ.
Lemma 3. If (1−g(h, 0, S))γS > CG, then there is a positive probability that G would reject.
Throughout this paper, we make the following assumption to rule out the possibility that
Google would always accept the claim no matter what her type is.
Assumption 2. (1− g(h, 0, S))γS > CG.
Assumption 2 implies that there is some lower bound on S. This is intuitive because
if S is too small, then rejecting (and subsequent litigation by P) will cause Google to win
litigation with a very small probability but with an additional litigation cost; therefore, any
type of G may as well accept the claim. Similarly, G’s litigation cost must not be too large.
In addition, the above assumption implies that the petitioner’s harm should not be too large,
because otherwise, if h is too large compared to S then even the highest type of Google may
not find it in her interest to reject the claim.
Under Assumption 2, some types of Google will always reject, and so, the total prior
probability of the path of play facing Google of type γ in the rejection state is strictly
positive, i.e., (1− F (γG)) > 0. Therefore, Bayes’ formula completely characterizes P’s belief
probabilities upon rejection.18 Upon rejection, the petitioner forms his posterior expectation
of γ given the posterior beliefs concentrated on [γG, γ], and decides whether to litigate or to
give up. In doing so, the petitioner’s strategy p2 must be optimal given Google’s optimal
cut-off strategy γG. The petitioner will be indifferent between litigating and giving up upon
rejection if and only if:
g(h, γ(γG), S)h− CP = 0. (3.4)
Let γ∗ be the unique value of γG that solves (3.4).19 It trivially follows that γ∗ > 0;
otherwise, Assumption 1 is violated.
18Because of Assumption 2, Bayes’ consistency implies full consistency of beliefs (i.e., the conditional prob-abilities that P faces Google of type γ given rejection). So upon rejection P determines his posterior beliefsusing Bayes’ formula.
19Note that ∂γ∗
∂h> 0, ∂γ∗
∂S< 0, and ∂γ∗
∂CP< 0.
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Lemma 4. The petitioner’s best response upon rejection is characterized as:
(i) p2 = 1 if γG < γ∗;
(ii) p2 ∈ [0, 1] if γG = γ∗; and
(iii) p2 = 0 if γG > γ∗.
Let γ∗G be the cutoff value γG for p2 = 1, i.e., γ∗G satisfies:
γ∗GS = g(h, γ∗G, S)γ∗GS + CG. (3.5)
We can now characterize a unique equilibrium to the continuation subgame following the
petitioner’s claim.
Proposition 1. Under Assumptions 1 and 2, there is a unique Nash equilibrium in the
subgame when the claim is made, in which the equilibrium strategies are characterized as
follows:
(1) if γ∗G < γ∗, then G of type γ ≥ γ∗G reject the claim, G of type γ < γ∗G accept the claim,
and P always choose to litigate, p2 = 1; and
(2) if γ∗G ≥ γ∗, then G of type γ ≥ γ∗ reject the claim, G of type γ < γ∗ accept the claim,
and P randomizes, choosing litigation with probability p2 = γ∗Sg(h,γ∗,S)γ∗S+CG
.
In addition, the posterior beliefs of P satisfy Bayes theorem upon rejection given the priors,
i.e., f(γ)1−F (γG) , where γG is the cutoff value of G’s strategy, and thus the posterior expectation
of γ upon rejection is E(γ|γ ≥ γG).
Proposition 1 describes the unique equilibrium in the subgame following p1 = 1. The
equilibrium strategies described above form the unique equilibrium in behavioral strategies.
Under Assumption 2, the rejection state occurs with positive probability under the unique
equilibrium, and thus the equilibrium strategies are always sequentially rational for P upon
rejection with the beliefs specified above.20 Figure 2 illustrates the best responses of Google
and the petitioner (Lemmas 2 and 4) in each of the two cases in Proposition 1.
20The beliefs are weakly consistent with the equilibrium in behavioral strategies. Because (1−F (γG)) > 0,rejection is never a zero-probability event and so weak sequential equilibrium implies full sequential equilibrium.
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Case (1): γ∗G < γ∗ Case (2): γ∗G ≥ γ∗
Figure 2: Best responses and Nash equilibrium
Consider now the petitioner’s initial node in which he has to decide whether to claim or
not. Because of Proposition 1, the petitioner compares his payoff from “no claim,” −h, with
his expected payoff from “claim” under the prior distribution of Google’s types given the
equilibrium strategies γG and p2 in the unique equilibrium of the subgame,
F (γG)(−c)+
(1− F (γG)) [(1− p2)(−h− c) + p2 (− (1− g(h, γ(γG), S))h− c− Cp)] .(3.6)
Then the petitioner’s optimal strategy at his initial node would be to claim if (3.6)≥ −h.
This condition reduces to:
c ≤ F (γG)h+ (1− F (γG))p2 [g(h, γ(γG), S)h− CP ] . (3.7)
As is evident from (3.7), if the primitives of our model were such that γ∗G ≥ γ∗, then given
the subgame equilibrium strategies specified in Proposition 1, (3.7) becomes:
c ≤ F (γ∗)h, (3.8)
whereas if the primitives were such that γ∗G < γ∗, then given the subgame equilibrium, (3.7)
becomes:
c ≤ F (γ∗G)h+ (1− F (γ∗G)) [g(h, γ(γ∗G), S)h− CP ] . (3.9)
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The intuition is straightforward: the claim fee has to be small enough for “claim” to be
profitable to the petitioner assuming that all moves after the claim would be determined
according the strategies specified in Proposition 1.
Proposition 2. Under Assumptions 1 and 2, for any given c, h, S, CP , and CG, P’s strategy
p1 such that p1 = 1 if (3.7) holds and p1 = 0 if otherwise, together with the strategies and
beliefs described in Proposition 1, constitute a unique sequential equilibrium of the RTBF
game.
The intuition simply follows: When a petitioner supposedly suffered harm from the links
that are on a web search engine, then as long as the claim fee is small enough, the petitioner
(regardless of the size of his harm) will act aggressively and claim his right to be forgotten, in
hopes of his claim being accepted and, despite rejection, of winning in court, both of which
will lead to broken links.
4 Higher Users’ Welfare Loss
In this section, we examine the effect of a change in users’ welfare loss S (when links are
removed) on the probability of lawsuits, the likelihood that the case will be settled in court
once the claim has been made. This allows us to calculate the likelihood of “broken links” as
a final outcome in equilibrium.21
4.1 The Effect on the Probability of Lawsuits
One might naively reason that if there is a higher welfare loss to users from broken links
relative to the petitioner’s harm, then the petitioner should expect to lose the trial with a
higher probability and litigation becomes less likely. However this is almost surely not the
case because the petitioner can commit to litigate with probability one up to a sufficiently
large S.
Formally, the probability of lawsuits in the unique equilibrium of the subgame following
21Another important factors that shape the probability of lawsuits and the likelihood of broken-links arethe magnitude of the parties’ litigation costs. The comparative static results regarding the effects of higherCG or CP can be found in Subsection 7.1.
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the petitioner’s claim can be calculated as follows:
Pr(“lawsuits”) ≡ (1− F (γG))p2
=
(1− F (γ∗G)) if γ∗G < γ∗,
(1− F (γ∗))
(γ∗S
g(h, γ∗, S)γ∗S + CG
)if γ∗G ≥ γ∗.
(4.1)
Note that the total prior probability that G will reject the claim is 1 − F (γG), where G’s
optimal cutoff value γG (either γ∗G or γ∗) decreases in S. Therefore according to G’s optimal
cutoff strategy, (1 − F (γG)) increases in S with a kink at γ∗G = γ∗. Also notice that in
equilibrium the probability that P litigates is p2 = 1 when γ∗G < γ∗, whereas p2 decreases
with S when γ∗G ≥ γ∗. Otherwise in the latter case, if P were to commit to litigation, then
G with types γ ≥ γ∗G will reject, in which case P’s litigation becomes unprofitable and so
his commitment to litigation is not credible. That is, rejection by less of high types provides
more information that P’s case is weak. Therefore P must lower his probability of choosing
“litigate” so as to make more types of G reject. In particular, he would litigate with a
lower probability just enough to make G of type γ = γ∗ ≤ γ∗G indifferent.22 His now-lower
probability of litigating implies a greater chance of being rejected; but after rejection he
was correct to litigate according to such probability, which confirms P’s indifference between
litigation and give-up.
Define S∗ to be the value of S such that γ∗G = γ∗ given other primitives. The following
proposition shows the effect of an increase in S on the probability of lawsuits in the unique
subgame equilibrium following P’s claim.
Proposition 3. For given h, CP , and CG, the probability of lawsuits increases with a small
increase in S if S < S for some S ∈ [S∗, S); and the probability of lawsuits decreases with a
small increase in S if S ≥ S.
Proposition 3 implies that the probability of lawsuits achieves its maximum at a unique
S ∈ [S∗, S). This is illustrated in Figure 3.
22This can be easily observed in Figure 2 Case (2): As γ∗ falls by an increase in S (the red horizontal lineshifts down), then p2 in Nash equilibrium, which is the fixed point of the best responses, decreases. Note thatas S approaches S, γ∗ → 0 and so p2 → 0.
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Figure 3: The effect of S on the probability of lawsuits in equilibrium
The intuition is as follows. Generally when S increases, the probability of G’s rejection
increases, and so P’s posterior assessed probability of winning in a trial decreases, in turn
lowering P’s expected payoff of the trial with his posterior concentrated on [γG, γ]. When
S < S∗, even though P’s expected payoff from litigation falls by an increase in S, the increased
S is not large enough to make litigation unprofitable compared to giving up and thus P can
still maintain to act aggressively – litigate with probability one. Therefore a higher S in
this case has a correspondingly higher chance of being rejected by Google, and the petitioner
always proceeds to court. On the other hand, if S increases when S ≥ S∗, the increased
probability of G’s rejection makes P’s litigation unprofitable compared to giving up. This
implies that P would no longer be able to litigate with probability one; thus upon rejection,
P would have to litigate less often to compensate for his loss from litigation. Such fall in P’s
probability of litigation more than offsets the increased probability of rejection by G when
S ≥ S. Therefore, the overall probability of lawsuits fall.23
4.2 The Effect on the Likelihood of Broken Links
We now assess the likelihood of broken-links as a resulting equilibrium outcome. Consider
again the equilibrium path after the petitioner has made the claim. The links are removed
23Under a certain condition on the right derivative of the probability of lawsuits evaluated at S = S∗, themaximum occurs at the kink γ∗G = γ∗, i.e., S = S∗. The condition is given in the proof of Proposition 3.
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in either of the following cases: (i) Google accepts the claim; or (ii) Google rejects, the
petitioner litigates and wins. Therefore, we can compute the expected likelihood of broken-
links as follows:
Pr(“broken links”) ≡ F (γG) + (1− F (γG))p2g(h, γ(γG), S)
=
F (γ∗G) + (1− F (γ∗G))g(h, γ(γ∗G), S) if γ∗G < γ∗,
F (γ∗) + (1− F (γ∗))
(γ∗S
g(h, γ∗, S)γ∗S + CG
)g(h, γ(γ∗), S) if γ∗G ≥ γ∗.
(4.2)
The following proposition shows how a change in S affects the likelihood of broken-links.
Proposition 4. The likelihood of broken-links unambiguously decreases with an increase in
S, for given h, CP , and CG.
The result is straightforward. When more welfare is lost from broken links, the outcome
of broken links becomes less likely. However to understand the intuition behind the course of
such effect better, we need to consider two channels through which an increase in S separately
affects the likelihood of broken-links, decomposed as follows:
F (γ∗G)︸ ︷︷ ︸(1)
+ (1− F (γ∗G))g(h, γ(γ∗G), S)︸ ︷︷ ︸(2)
if γ∗G < γ∗.
(1) As S increases, less types of Google accept, i.e., F (γ∗G) decreases, contributing to less
chance of broken links;
(2) At the same time, more types of Google reject and the expected probability of the
petitioner winning in court falls, so whether Term (2) rises or falls is ambiguous.
Regardless, the first effect is stronger than the second effect because P’s expected winning
probability is less than one, so that a decrease in Term (1) more than offsets any increase in
Term (2). Similarly for the second case:
F (γ∗) + (1− F (γ∗))
(γ∗S
g(h, γ∗, S)γ∗S + CG
)︸ ︷︷ ︸
=Pr(“lawsuits”)
g(h, γ(γ∗), S)︸ ︷︷ ︸(∗)
if γ∗G ≥ γ∗.
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As is evident from the previous discussion, the first term F (γ∗) decreases with S while (1−
F (γ∗)) increases. Even if Pr(“lawsuits”) may increase for S ∈ [S∗, S), the marginal increase
is less than the marginal decrease in the first term. Moreover, the expected probability of
P winning (Term (*)) is constant (and less than one) for any S. The reason is that when
γ∗G ≥ γ∗, P is just indifferent between litigation and give-up after rejection by the types
γ ≥ γ∗, implying that his (posterior-assessed) probability of winning must remain the same
regardless of a change in S.24
In either case, an increase in S unambiguously lowers the likelihood of broken-links with
a kink at S = S∗. Figure 4 illustrates this comparative static result.
Figure 4: The effect of S on the likelihood of broken-links in equilibrium
An obvious implication is that if higher welfare is lost from broken links, the petitioner
“correctly” expects to win the case less often, but he can still credibly “threat” to litigate
with probability one even for a considerably large amount of users’ welfare loss; and as a
result, an excessively more number of claims are rejected and brought to court. Nonetheless,
the court is more likely rule in favor of Google, which together with less Google’s immediate
acceptance of the claim primarily contribute to lower chance of broken-links. This effect is
exacerbated when users’ welfare loss is so high such that the petitioner starts to give up more
often.
24Given G’s optimal cutoff strategy with the cutoff value γ∗, P’s posterior expectation of γ on the interval[γ∗, γ] decreases as more types reject by an increase in S.
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5 Social Welfare and Efficiency
Our equilibrium and comparative static results provide an interesting observable implica-
tion that answers the following questions: Are there too many or too few links delisted at
equilibrium in terms of social efficiency? Does the number of requests for removal that are
submitted exceed the socially optimal amount?
5.1 Optimal Probability of Broken Links
Suppose now that a social planner considers the (ex-post) social welfare maximization prob-
lem,25 where ex-post social welfare is given by the total payoffs of all associated individuals
(the petitioner with harm level h, Google of type γ, and network users) less fixed costs. When
the links are taken down, the ex-post social welfare loss is γS + S, whereas when the links
remain, the ex-post social welfare loss is h. Thus the social planner’s decision would depend
on whether or not h (welfare saved by taking down the links) is higher than γS + S (welfare
saved by retaining the links). In this sense, we can then interpret h as the social value of the
right to be forgotten (or, the right of privacy) and γS + S as the social value of the right to
remember (or, the right of free speech and access to information plus Google’s right to do
business).
For any given h, γ, and S, if h > γS + S, the social efficiency calls for the links to be
delisted – “favoring” the right of privacy over the right of free speech, expression, and access
to information; if otherwise, the links to be retained. This implies that there exists a socially
optimal cutoff value of γ such that if Google’s type is below such cutoff, then the social
planner would require removal; otherwise retention is required. We define this value as the
social planner’s efficiency cutoff, denoted by γe, such that:
γe =
γ if h ≥ γS + S,
h−SS if S < h < γS + S,
0 if h ≤ S.
(5.1)
25A social planner is represented by the omniscient benevolent dictator. By ex-post, we mean that claimfee and litigation costs are not included in the social planner’s problem. This restriction does not derive theresult, but is in line with the litigation literature.
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Therefore, for given h and S, γe can be interpreted as the highest possible type of Google
against whom the social planner would dictate removal. Accordingly, the socially efficient
probability of broken-links is given by Pre(“broken links”) ≡ F (γe).
Let Pr∗(“broken links”) denote the expected probability of broken-links evaluated at
equilibrium, given in (4.2). Then in terms of social efficiency, if Pr∗(“broken links”) <
Pre(“broken links”), then too few links are expected to be broken in the equilibrium; if
Pr∗(“broken links”) > Pre(“broken links”), then too many links. In order to describe
whether there are too many or too few links taken down in the equilibrium of our RTBF
game, we shall adopt the following definitions. We will refer to an equilibrium in which the
petitioner claims, i.e., c is such that (3.7) is satisfied, as a claim equilibrium. An equilibrium
is a no-claim equilibrium if otherwise. In the claim equilibrium, the social planner’s “assess-
ment” of the petitioner’s winning probability upon rejection by types γ ≥ γG can be defined
as follows:
ge(γe; γG) ≡
F (γe)−F (γG)
1−F (γG) if γG ≤ γe,
0 if γG > γe.
(5.2)
We arrive at the following results.
Proposition 5. For given h and S:
(i) In the claim equilibrium,
Pre(“broken links”) > Pr∗(“broken links”) if g(h, γ(γG), S) < ge(γe; γG);
Pre(“broken links”) < Pr∗(“broken links”) if g(h, γ(γG), S) > ge(γe; γG).
(ii) In the no-claim equilibrium,
Pre(“broken links”) > Pr∗(“broken links”) = 0 if h > S;
Pre(“broken links”) = Pr∗(“broken links”) = 0 if h < S.
Proposition 5(i) implies that too few (many) broken links are expected to arise in the
claim equilibrium if the petitioner underestimates (overestimates) the his winning probability
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in court.26 When g(h, γ(γG), S) = ge(γe; γG), the expected probability of broken-links in
equilibrium exactly coincides with the socially efficient probability of broken-links because
the petitioner “correctly” updates his belief on the types of Google who would reject, against
whom the social planner would dictate removal. In such case, the amount of broken links in
the claim equilibrium achieves social efficiency.
For the no-claim equilibrium, it is somewhat more obvious: If the petitioner’s harm is
greater than network users’ welfare loss, then (5.1) implies that the social planner would find
at least some (lower) types of Google who should be dictated to remove the links but against
whom the petitioner had not filed the claim in the first place; On the other hand, if otherwise,
then the social planner would prefer retention of the links even against the type of Google
who loses nothing, and so the no-claim equilibrium coincides with what social efficiency would
dictate.
Figure 5: Equilibrium vs. optimal probability of broken-links
Figure 5 illustrates Proposition 5(i) for given h in terms of S. Our model shows that in
equilibrium there may be too many or too few broken links compared to the socially optimal
amount of broken links that maximizes the ex-post social welfare. The case of too few broken
links occurs when S is relatively small; the opposite happens for a relatively larger S.
26In other words, too few (many) broken links arise in the claim equilibrium if the petitioner’s posteriorexpectation of γ upon rejection is less (greater) than the highest possible type against whom the social plannerwould dictate removal.
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Beyond the theoretical underpinning, Proposition 5 suggests a testable empirical study
with the real world data. Let us assume an ideal situation in which one could collect all
factual information on the true values of h, γ, and S. Based on these information, the ex-
post efficient rule can be established, which would depend on the relative values of h and
(γ + 1)S. Then we can compare the actual rulings in the RTBF cases with what the ex-post
efficiency would rule. The outcomes of the actual rulings would essentially be either of the
following two cases: (i) the links remain uncut when they should have been removed from
a social efficiency perspective; or (ii) the links are taken down when they should have been
retained. If we find that the first cases occur far more than the second, then it may imply that
the right to be forgotten is under-protected relative to the efficient level. On the other hand,
if the second cases prevail, the right to be forgotten is threatening the right to remember
beyond the properly balanced level. Therefore we might be able to evaluate the rulings in
the current RTBF cases in terms of social efficiency.
5.2 Excessive Number of Claims
Continuing from the previous analysis, we can also consider efficiency with regard to the
number of claims. As implied by Propositions 1 and 2, the petitioner tends to act aggressively
and file the request for removal as long as his claim fee is small. Therefore we might reasonably
expect that the number of requests submitted to Google exceeds the socially optimal amount
for some range of values, which is exactly what happens in the RTBF game as discussed in
this subsection. We start by the following proposition.
Proposition 6. For given h and S, if γe < γ, then the claim equilibrium renders an excessive
number of claims that are brought to a trial. Moreover if γe < γG, then the claim equilibrium
renders an excessive number of claims that are accepted by Google, as well as those that are
brought to a trial.
The proof is obvious. The first threshold condition in Proposition 6 implies that γS+S >
h for all γ ∈ (γe, γ]. So if the social planner, who finds out that Google is of such type in
the RTBF game, would dictate to the petitioner with harm h not to request the removal in
the first place so that the links are not removed. In this sense, too many requests for the
removal of links are brought to court and resolved by costly court-imposed judgments. The
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second threshold condition implies that there exists γ ∈ (γe, γG) such that γS +S > h. So if
the petitioner’s claim is submitted to such type, social efficiency calls for the claim not to be
accepted immediately. In fact, the claims that are made to and accepted by Google of types
γ ∈ (γe, γG) and the ones that are rejected by Google of types γ ∈ [γG, γ] should not have
been in place.
On the other hand, if γe = γ, i.e., the efficiency cutoff is exactly the highest type of
Google, then h ≥ γS + S for any γ ∈ [0, γ]. In such case, the petitioner was correct to file a
claim in the sense that the social planner would prefer the petitioner to claim versus no-claim
against any type of Google.
Figure 6: Excessive amount of claims
Proposition 6 is illustrated in Figure 6, which plots the social planner’s efficiency cutoff
and Google’s optimal cutoff value of her equilibrium strategy in relation to S. The shaded
area above the efficiency cutoff indicates the types of Google against whom social efficiency
would require the links to be retained for given h and S. Therefore the social planner, who
finds out that Google is of type γ > γe, would dictate the petitioner with harm h not to
file a claim in the first place (or more generally retention of the links). We can see that too
many claims are filed and eventually brought to costly litigation when S > hγ+1 ; and too
many claims are accepted by Google when S > hγG+1 , in terms of efficiency, the observations
of which confirm our claims in Proposition 6.
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6 The European Ruling and the Debate on Expansion
In this section, we discuss the following questions: (1) How do our model and equilibrium
results connect to explaining the initial European ruling on Costeja case and the subsequent
launch of Google’s online request process within Europe? (2) Could our results provide a
reasonable prediction of individuals’ behavior of removal request and Google’s response in
delisting the links when the European ruling is applied to all of Google’s global search engine
domains?
In answering these questions, we simplify our model by assuming that γ is drawn from
a Uniform distribution F (·) over the interval [0, 1]. We further assume g(h, γ, S) = hh+γS+S
for analytical tractability.27 Accordingly, we give a numerical example that maps our model
into the economics behind the current situation since the European ruling; in doing so, we
first justify the case that initially led to the European ruling and set a major precedent over
the issue of the right to be forgotten in terms of our model. Finally, under our model, we
describe the effect of the expansion of the right to be forgotten to non-European websites.
For the first question, let us assume that Costeja (petitioner) suffers harm of size h = 150
from the defamatory links remained on Google’s search results. So Costeja first requested
Google Spain that the links to be removed; Google Spain then forwarded the request to
Google Inc. When that was unsuccessful, Costeja eventually brought the case to court.
The court considered the scope of removal to be all Google domains on a global basis. To
capture this situation, suppose that if the links for queries that include Costeja’s name are
delisted from all Google domains, then network users’ welfare loss is SW = 100; and Google
internalizes users’ loss as her own profit loss by γSW , where the profit-loss rate γ is private
information. Costeja believes that Google’s profit-loss rate is uniformly distributed on [0, 1]
Finally suppose that litigation costs for both parties are CP = CG = 10.28 Then our model
yields the following equilibrium strategies of Costeja and Google:
• Costeja claims if c ≤ 81.84, and always litigates;
• Google would reject the claim if γ ≥ 0.22, otherwise accept.
27We give a clear exposition of Propositions 1 and 2 under these simplifying assumptions in Online AppendixB.
28We can think of all the parameter values in terms of monetary unit.
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Therefore if we assume that Costeja’s initial claim fee was reasonably less than 81.84 and
Google’s profit-loss rate were greater than 22 percent, the above equilibrium submits the
actual sequence of events in the Costeja case: Costeja first requested, Google rejected, Costeja
then sued Google, and so the case resorted to the court-imposed judgment. For illustration,
let Google’s true profit-loss rate to be fixed at 30 percent from any delisted information. Once
the case was actually proceeded to a trial, the ECJ gathered all the relevant information and
the process of discovery revealed Google’s true loss; in fact the ECJ “efficiently” ruled in favor
of the petitioner because the ex-post social welfare loss from the broken links ((γ+1)S = 130)
was less than the ex-post social welfare loss from the links (h = 150).
Now in order comply with the European ruling, Google launched the online request pro-
cess. When an individual makes a request for search removals through a web-form, Google
evaluates whether the results include outdated or inaccurate information about the person
and weighs whether there is a public interest in the information remaining in search results;
Google may decline to remove certain information, and if so an individual may request a data
protection authority to review Google’s decision. Since its first day of compliance, Google
received more than 219,000 claims and has accepted about 40 percent of the total URLs
requested for removal, delisting more than 795,000 URLs.
A notable aspect in Google’s compliance is its interpretation of the ECJ ruling that it is
an application of European law that applies to services offered to Europeans and not to global
in reach. Based on this interpretation, Google in fact restricted its compliance to the local
subsidiary for which the requester is associated with. In particular, the requesting individual
will need some connection to one of EU and EFTA countries, and Google would remove the
links from search results only in European versions of Google search services. Therefore when
Google evaluates whether to remove the links or not, it will assess network users’ welfare loss
pertaining only to the local domain.
Taking this into account, we assume that if users’ welfare loss from the broken links of
searched results on a certain name in all Google domains on a global basis were SW = 100
(as in the Costeja case), then the broken links only in a local Google domain would result
in a lower welfare loss, say SL = 70. Then our model predicts the following strategies of a
petitioner and Google:
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• The petitioner with harm h = 150 claims if c ≤ 101.88, and always litigates;
• Google would reject the claim if γ ≥ 0.37, otherwise accept.
The above example illustrates several interesting observations when network users’ social
welfare loss is SW = 100 in comparison to when SL = 70, given any petitioner with a fixed
harm level of h = 150. We list these in terms of our results in Sections 4 and 5 as follows:
1. The petitioner would expect Google to accept his request with a higher probability
of 0.37 when SL = 70 than the probability of 0.22 when SW = 100. In both exam-
ples, the petitioner litigates with probability one upon rejection. Thus the equilibrium
probability of lawsuits is 0.63 when SL = 70, which is less than 0.78 when SW = 100.
2. The petitioner’s expected probability of winning in court29 is
g(150, γ(0.37), 70) = 0.56 > 0.48 = g(150, γ(0.22), 100).
Then the ex-ante likelihood of broken links is 0.72 (= 0.37+0.63·1·0.56) when SL = 70,
which is greater than 0.60 (= 0.22 + 0.78 · 1 · 0.48) when SW = 100.
3. Social efficiency implies that the claim should be made against any type of Google when
SL = 70, but only against Google of types γ < 0.5 when SW = 100.30 This implies
that in the latter case, the petitioner’s claim may have been excessive in the sense
that it could be inefficiently be brought to court and resolved by costly court-imposed
judgments.
4. The socially optimal probability of broken-links is one when SL = 70, while it is 0.5
when SW = 100. Together with (2), this implies that too few broken links are expected
to arise in equilibrium when SL = 70, while too many links are expected to be broken
in equilibrium when SW = 100.
29Those types of Google who accept (γ < 0.37) estimates the petitioner’s winning probability to beg(150, γ, 70) ∈ (0.61, 0.68] and those types who reject (γ ≥ 0.37) estimates g(150, γ, 70) ∈ [0.52, 0.61], whenSL = 70; whereas when SW = 100, those types who accept (γ < 0.22) assesses g(150, γ, 100) ∈ (0.55, 0.60]and those types who reject (γ ≥ 0.22) assesses g(150, γ, 100) ∈ [0.43, 0.55].
30Social efficiency calls for the links to be broken if h > γS + S. This implies that the petitioner shouldnot have filed the claim in the first place against Google with type γ ≥ h−S
S. Note that when SL = 70,
(γ + 1)70 < 150 for all γ ∈ [0, 1].
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5. If Google’s true profit-loss rate is γ ∈ [0.22, 0.37) for any delisted information, then
Google accepts the claim when SL = 70 when she would have rejected it if SW = 100.
How could our model explain Google’s immediate acceptance without being brought to
legal authorities or to court over the past few months? The above example provides a nu-
merical equilibrium prediction regarding Google’s removal request process: The likelihood of
Google’s acceptance of a claim is about 37% for given h = 150 and SL = 70. We note some
caveats in this observation. First, the question of whether the remaining 63% of rejection has
been proceeded to a data protection authority or court and how those were resolved are unan-
swered. Nonetheless, we can expect a priori about 72% of the links would be delisted if every
requester appeals against Google’s rejection decision; if the court correctly and efficiently
rules in favor of the requester, then every claim will result in broken links.
Second, we described the equilibrium consequences in a game between Google and a
petitioner with a fixed level of harm; however Google’s removal request process is used by
petitioners with different sizes of harm from the links that give various levels of welfare to
network users.31 Therefore a complete description of the current situation should involve
an analysis of the probability of acceptance given some distributions of h and S. Such
analysis is, in principle, technically feasible; however simplicity of our model makes the
fundamental issues in the RTBF game easier to see than the more complicated analysis,
and thus our “simple” model can give a reasonable description of petitioners’ and Google’s
behaviors without ignoring vital aspects of the real games.
The intuition behind this second point may be described as follows. Assumption 1 implies
a lower bound on h such that litigation is profitable to the petitioner given the prior distribu-
tion of Google’s types. If this assumption is relaxed, then there is still a unique equilibrium
to the RTBF game such that the petitioner always chooses not to claim if h ≤ h. Of note
is that h increases with S, which implies that those petitioners with h ≤ hW who did not
claim at all when SW = 100 would now be able to make a claim when SL = 70 as long as
h > hL and the claim fee is small enough, and Google would accept the claim with positive
probability. Also Assumption 2 gives a sufficient condition on an upper bound of h for which
there is a positive probability that Google would reject. If this assumption is relaxed, then
31A petitioner’s harm and network user’s welfare loss are not necessarily correlated. We will briefly commenton this in Subsection 7.4.
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when the petitioner with a sufficiently large h claims, Google would always accept the claim
no matter what her type is. Such upper bound h also increases with S, which implies that
those petitioners with some high levels of harm whose claims were rejected with positive
probability when SW = 100 would now be able to make a claim that is always accepted when
SL = 70. These considerations imply that for a smaller network users’ social welfare loss,
(i) more claims would be made by petitioners with small harm and would be accepted with
positive probability, and (ii) more claims by petitioners with large harm would be accepted
with probability one; both of which contribute to greater acceptance by Google and thus
more broken links.
Third, note that Google has actually processed 40.4% of removal requests according to
its recent transparency report. One explanation involves chilling effects due to one of the
features in the Principles of European Tort Law (PETL): the European ruling essentially
puts the burden of proof on data controllers under the provision of PETL. That is, the data
controllers must prove that the retention of the links is necessary for exercising the right of
free speech and falls under the category specified as an exemption from the duty to remove.
What this means is that a data controller, upon receiving requests, must take every possible
means to evaluate each case; and if the requester confronts a rejection decision, then the data
controller is fined a considerable amount of penalty if it did not comply with the rules in the
RTBF standards. Thus data controllers may more often opt for removal of the links than
otherwise would have.32 Although the equilibrium strategy of Google when SL = 70 demands
only the types γ < 0.33 should accept, some higher types might as well immediately accept
the request in fear of monetary sanctions rather than fighting for the retention of potentially
ambiguous contents.
Notwithstanding these issues, we can explain how the equilibrium consequences are influ-
enced by Google’s compliance restricted to local domains in terms a change in network users’
welfare loss from delinked information. By reverse-engineering, we can equally examine how
the global expansion might affect the expected chance of broken links. The emerging debate
regarding the right to be forgotten is on whether the European ruling should apply far more
32Rosen (2012b) mentions that “the prospect of ruinous monetary sanctions for any data controller that“does not comply with the right to be forgotten or to erasure” – a find up to 1,000,000 euros or up to twopercent of Facebook’s annual worldwide income – could lead data controllers to opt for deletion in ambiguouscases, producing a serious chilling effect” (pp.90-91).
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Kim & Kim: The Right to be Forgotten
broadly than originally understood. Should Google impose the right to be forgotten decision
on all of its global search results? The central issue at hand is a clash between European
and American conceptions of privacy rules. Privacy watchdogs in the European Union have
already issued guidelines in September 2014 calling on Google to apply the European ruling
to its entire search engine. However the guidelines are not binding, and Google’s indepen-
dent advisory council is expected to recommend that Europe’s privacy standards should only
apply within Europe.
In the midst of the battle over whether people have the right to be forgotten online, our
model may provide an interesting prediction of what would happen if Google expands the
scope of link removals to all of its domains. As noted earlier, our key presumption is that if
the European ruling is imposed also on sites that operate outside Europe, then network users’
welfare loss from globally delisted links would become larger. This implies that Google would
reject more removal requests while it already rejects about 60%. If the requester disagrees
with Google’s initial decision and resort to national data regulators, then more number of
cases would proceed to costly litigation. At the same time, because the relative value of the
right to be forgotten would lessen, the court would be more likely to find for Google. Thus
our model predicts that the expansion of the European ruling would actually contribute to
less number of links delisted.
Furthermore, our discussion of efficiency in Section 5 renders a rather surprising policy
implication on how to deal with the expansion of the right to be forgotten. Applying an
empirical test briefly discussed, if the current ruling is not strong enough to protect the
right to be forgotten and thus too many defamatory links remain uncut, the expansion will
be hardly justified as an effort to strengthen the protection of the right to be forgotten as
argued by some European data regulators. By contrast, if too many links are taken down
under the current legal standard, the expansion may help to get close to the efficient outcome.
The advocates for freedom of speech and access to information stress that the European
legal decision unjustly limits what can be published online. The expansion of European
privacy rights may certainly allow increasingly more individuals to take Google and other
search engines to court to force them to remove links from global search results; However the
concern that the right to be forgotten is a threat to free speech on the internet is superfluous.
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Kim & Kim: The Right to be Forgotten
Our analysis of the underlying economics implies that the expansion might actually strike
an optimal balance between privacy and free speech: empowering individuals to manage and
control their personal data while protecting freedom of speech, expression, and access to
information by optimally retaining disclosure of information that is of public interest. In
fact, individuals can simply use a non-European web address whatsoever if only the links on
European sites are removed, while the expansion allows less of the overall links delisted in
the first place.
7 Discussions
7.1 Higher Litigation Costs, Lawsuits, and Broken Links
Because our RTBF game is featured as a legal dispute, the probability of G’s rejection and
the probability of P’s litigate are shaped by various factors – one of them being the magnitude
of the parties’ litigation costs. Here we discuss the effect of changes in litigation costs on the
probability of lawsuits and the likelihood of broken-links in equilibrium. In fact, the results
are closely in line with Bebchuk (1984)’s comparative statics with a subtle difference.
Note that Assumptions 1 and 2 imply upper bounds for CP and CG, respectively. Denote
CP and CG to be the corresponding upper bounds, for given values of h and S; and let C∗P
and C∗G denote the values of CP and CG such that γ∗G = γ∗. Because CP ∈ (0, CP ) and
CG ∈ (0, CG), the subsequent results will hold for marginal changes in the parameters within
the relevant range.
Proposition 7. (a) The probability of lawsuits decreases in CG for any CG ∈ (0, CG); The
likelihood of broken-links increases in CG if CG ∈ (0, C∗G), but decreases in CG if CG ∈
[C∗G, CG). (b) Both the probability of lawsuits and the likelihood of broken-links are not affected
by a change in CP if CP ∈ (0, C∗P ); both decrease in CP if C ∈ [C∗P , CP ).
The traditional comparative static results continue to hold for the effect of changing
Google’s litigation costs on the probability of lawsuits: The probability of lawsuits unam-
biguously falls when Google’s litigation cost increases.33 This is straightforward because, for
33Bebchuk (1984) shows that “an increase in the litigation costs of either party will increase the likelihoodof a settlement” (409). The counterpart of the likelihood of a settlement translated into our setting is 1 −Pr(“lawsuits”).
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any type, Google’s expected payoff from litigation becomes smaller with a higher litigation
cost. A rather interesting observation is that an increase in Google’s litigation cost (up to
a certain point) causes Google more likely to accept the petitioner’s claim, creating more
chance of broken links despite a relatively low petitioner’s winning probability.34 Only when
Google’s cost is sufficiently high so that the petitioner chooses to litigate less often results in
less chance of broken links. In this case, an increase in Google’s litigation cost leads the peti-
tioner to choose litigation with a lower probability that induces exactly the same interval of
Google’s types who would reject; in turn maintaining the same expected winning probability
for the petitioner. But now that the petitioner chooses litigation with less probability, which
leads to less chance of broken links.
One might expect that when the petitioner’s litigation costs increase, he would proceed to
court less often and so the probability of lawsuits also falls, which would lead to less broken
links. However, this is not always the case. A change in the petitioner’s litigation costs has
no effect on Google’s cutoff type, and so on the probabilities of acceptance and rejection, up
to a large amount of CP .35 Hence, the expected number of cases that proceed to court and
the chance of broken links remain constant. The intuition is that the types of Google who
reject are large enough (γ∗G < γ∗) – enough to compensate for the petitioner’s higher cost –
so that the petitioner believes that he still has a fair chance of winning in court and litigates
with probability one. However, when the petitioner’s litigation cost is high enough, if the
petitioner still maintains to litigate with probability one, then the cutoff type of Google is
high such that litigation becomes unprofitable; and so the petitioner must proceed to court
less often to induce more types of Google to reject. Then as the petitioner’s litigation cost
increases, less types of Google accept and those types who reject are faced with much less
probability of the petitioner’s litigation, both of which lead to a decrease in the likelihood of
broken-links.
7.2 Different Legal Rules on Litigation Costs
In all preceding analyses, we assumed the American rule of litigation costs – each party bears
his or her own litigation costs regardless of the trial’s outcome. Our model can be equally
34An increased acceptance by Google makes the petitioner’s inference about the case less favorable to himupon rejection, however the former direct effect dominates the latter indirect one.
35Note that when γ∗G < γ∗ (or CP < C∗P ), Google’s best response is independent of CP .
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used under the British rule, which governs that the losing party bears all the litigation costs.
Hence, we can examine how the probability of lawsuits and the likelihood of broken-links are
affected by different legal rules. Bebchuk (1984) similarly examines the effects of various legal
rules of litigation costs on the likelihood of settlement (i.e., the probability of acceptance),
but in a different setting in which the parties can settle out of court by choosing the optimal
settlement amount in a pre-trial negotiation environment.36
If the British rule is adopted in our model, the expected payoffs from litigation become
−(1 − β)(h + CP + CG) − c for the petitioner and −β(γS + CG + CP ) for Google, where
β = g(h, γ, S); all other specifications of the model are maintained. Then we obtain the
following result.
Proposition 8. A change from the American rule to the British rule might increase, decrease,
or has no effect on the probability of lawsuits and the likelihood of broken-links.
Proposition 8 implies that the effects of different legal rules governing the allocation
of litigation costs on the probability of lawsuits and broken links are ambiguous. We find
some interesting underlying economics behind this result. First, a change to the British rule
unambiguously lowers the petitioner’s optimal cut-off type of Google, γ∗, that makes him
indifferent between litigating and giving up upon rejection by types greater than such cut-
off. This is because the amount that depends on the trial’s outcome is larger under the British
rule than under the American rule; hence, the marginal benefit to the plaintiff from litigating
against a low type than against a high type is greater under the British rule. Therefore, the
petitioner would want more (lower) types of Google to reject under the British rule in order
to limit Google’s ability to signal the weakness of the petitioner’s case.
However, whether Google’s cutoff value γG of her equilibrium strategy rises or falls is
ambiguous. To understand this, we need to note that Google’s expected payoff from litigation
also depends on CP under the British rule because the petitioner’s litigation cost becomes
Google’s burden when she loses the trial. Under the British rule, Google will suffer a loss of
γS+CG +CP if she loses and will bear no loss if she wins, whereas under the American rule
36Bebchuk (1984) focuses on how an informational asymmetry might influence parties’ litigation and settle-ment decisions and how it might lead to a failure of settlement. Among the results is that the likelihood thata case will end up in litigation is lowest under the American rule and greatest under the British rule.
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she will suffer a loss of γS+CG if she loses and will pay CG if she wins. We give the intuition
by comparing these arrangements for the cutoff type, γAG, that is indifferent between accepting
and rejecting under the American rule.37 If CP is sufficiently high, then considerably larger
stake depends on the trial’s outcome under the British rule compared to the American rule;
and so the cutoff type γAG would prefer to accept, which implies that more types of Google
accept under the British rule. On the other hand, if CP is negligibly small, then when the
cutoff type γAG loses under the British rule suffers a loss that is just about what she would
have lost under the American rule, but pays nothing when she wins under the British rule
while she pays her litigation cost when she wins under the American rule. So the cutoff type
γA would prefer to reject, implying Google will reject more often under the British rule.
Thus the probability of lawsuits (and correspondingly the likelihood of broken links)
under the British rule may be greater or smaller than that under the American rule greatly
depending on the primitives of the model. This implies that examining whether the expected
number of cases that are brought to court would increase or decrease in equilibrium by a
different legal rule only complicates some details of the analysis without adding commensurate
insight. More importantly, regardless of legal rules, Propositions 1 and 2 still hold, which
implies that all the main insights of our analyses in Sections 4 and 5 carry over.
7.3 Two-sided Private Information
Our model assumes that h is known to all, but γ remains the search engine’s private infor-
mation. What if h is also private information the petitioner? For sake of discussion, suppose
that there are the two types of petitioners: h and h. Google believes that the petitioner is
of type h with probability λ and h with probability 1− λ. Then, our analysis for each type
of h can be considered two distinct cases with the single-type petitioner for each λ = 0, 1. In
general, for an intermediate λ ∈ (0, 1), the petitioner’s decision to litigate or not should be a
function of λ. Assuming that the full information case of λ = 1 ensures the litigation upon
rejection (i.e., p2 = 1), the petitioner will follow litigation upon rejection for a sufficiently
large λ by the continuity argument, whereby the equilibrium will be described as Proposi-
tion 1-1. As λ continues to fall, Google will adjust her strategy by rejecting the claim more
often. One interesting issue that may arise in this two-sided asymmetric information setting
37See the proof of Proposition 8 in Appendix A for details.
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is the petitioners’ signaling incentives, as is well documented by Daughety and Reinganum
(2014). For example, since Google’s decision must be based on the average type, some type
of petitioners, who did not claim if Google had known the exact type, may opt for claiming
because Google may accept the request in the two-sided asymmetric information. Obviously,
the analysis shall become considerably involved. Admitting this is an interesting theoreti-
cal subject, we think that eventually the equilibrium will be characterized by a variant of
Propositions 1 and 2. We leave this analysis for further research for now.
7.4 Correlation between Losses
For our base model, we assume that network users’ loss from the broken links S is not
correlated with the petitioner’s harm h. Justification comes from the fact that the petitioner’s
harm mostly depends on his own individual characteristics. For example, Costeja might have
relatively large harm than others in similar situations because as a lawyer he might lose some
potential clients due to search results on his blemished reputation in the past. However, it
is plausible to think of a positive correlation between the two: If a petitioner’s harm comes
from users’ search and the value of the right to remember increases with the search intensity,
we should expect that h is an increasing function of S. Then we can write h = δS, and the
likelihood of the petitioner’s prevailing in a trial would become β = g(δ, γ, S). This change
would not qualitatively affect our analysis.
Another plausible scenario is to consider a positive relationship between h and γS. That
is, a petitioner a higher harm level may expect larger Google’s loss from the broken links.
However as long as γ is Google’s private information, the petitioner must still form some
belief about Google’s type upon rejection and our analysis should still apply. Thus we assert
that our assumptions on h, γ, and S substantially simplifies the exposition while conveying
all the key insights of our model.
7.5 Threats to Reputation Capital
The right to be forgotten laws can be seen as offering a “reset” over an individual’s damaging
reputation. While a second chance for an individual’s mistake should be regarded as a
respectable social value, it makes inevitable conflicts with the right of others for public
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information to assess the risks involved in dealing with someone.38 Remarkably, no one
could deny the significance of so-called ‘reputation capital’ in our information-based economy:
Customers look for reviews and ratings on goods and services. Employers get opinion on
potential employees. Business works hard to build strong positive reputation, for it thrives
with good reputation and withers with bad one. As much as the reputation capital is a vital
in decision-makings, any distortion in inference from reputation should be deeply damaging.
We briefly demonstrate how a broken link challenges the reputation system. Let us
consider a client who looks for a professional such as a lawyer, a consultant, an accountant, etc.
There are two types of professionals, efficient type (E) with probability θ and inefficient type
(I) with 1−θ, where θ measures the client’s prior belief of meeting the efficient. Assume that
type E professionals have positive reputation with probability πE but blemished reputation
with probability 1−πE , whereas type I professionals have positive reputation with probability
πI < πE . Then, using the Bayes’ rule, we can easily show that the posterior belief on type E
decreases as some type I professionals “reset” their reputation. This implies the efficacy of
positive reputation in identifying a better professional declines with the stronger the right-
to-be forgotten enforcement. Furthermore, because the return to better reputation decreases
when the links to information pertinent to blemished reputation can be easily washed out,
the incentives to build up or maintain clean reputation would weaken. In this aspect, the
value of the right to remember can broadly include any negative effects of the broken links
on the system of reputation capital.39
8 Concluding Comments
We are living in a world where an individual’s online activity can leave behind “digital foot-
prints” that can never be forgotten and other users can generate “data shadows” by spreading
the digital footprints without permissions.40 The Big Data is built upon digital footprints
38The Freeman, The Internet Memory Hole “The right to be forgotten” — a privacy right or Orwellianincinerator? NOV. 24, 2014 by WENDY MCELROY
39As a related point, people argued that the expansion of the European right to be forgotten into the globemay lead to more censorship by public officials such as autocrats who want to whitewash the past or removelinks they don’t like. Focusing on the economics of the right to be forgotten, we do not take such concerns intoaccount throughout this article. For this point, we refer to the N.Y. TIMES Editorial, Europe’s Expanding‘Right to Be Forgotten’, Feb. 5. 2015.
40See Koops (2011).
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Kim & Kim: The Right to be Forgotten
and data shadows, and the right to be forgotten is becoming an extremely important issue.
Threats to privacy in the era of open internet are far more ubiquitous than the threats from
back-then new technologies of Kodak camera and the tabloid press. In the canonical article
on the right to privacy, Warren and Brandeis (1890) made the following warning: “The press
is overstepping in every direction the obvious bounds of propriety and of decency. Gossip
is no longer the resource of the idle and of the vicious, but has become a trade, which is
pursued with industry as well as effrontery” (pp.195-96). At the heart of the current issue
of the right to be forgotten, a deeper stake is found: how to protect a personal dignity from
easier exposure and more difficult erasure.
The right to be forgotten is to protect the private dignity by making the erasure easier.
However this right may well make a fundamental conflict with the right to remember – free
speech and access to information. The value of dignity is a socially constructed value,41 so
much so the values of the right to remember. Consequently, it is not surprising to see wide
variations in evaluating the right to be forgotten, as is highlighted in the diametrical positions
between the European Union and the U.S. on the scope of privacy rights. Not only across
countries but also over time, the socially constructed values may change, which implies that
the debate over the right to be forgotten is expected to intensify.
In this paper, we pioneer an economic analysis of the right to be forgotten and offer a novel
framework in examining the impact of the expansion of the European standards on the right
to be forgotten. We contend that the expansion should be understood by analyzing an optimal
balance between privacy and free speech, rather than by a power game between European
data regulators and the dominant search engine, or by a clash between the European privacy
rule and the American First Amendment. If we could quantify privacy protection as the
number of links removed, then our analysis demonstrates that the expansion does not pose
a threat to the right of free speech. In any case, it is the authors’ opinion that our paper
should be taken as only a first step in an attempt to build the economics behind the right to
be forgotten, and we hope other works would follow and complement ours.
41See Rosen (2012a).
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Kim & Kim: The Right to be Forgotten
References
Ambrose, M. L., and J. Ausloos (2013): “The right to be forgotten across the pond,”
Journal of Information Policy, 3, 1–23.
Bebchuk, L. A. (1984): “Litigation and Settlement under Imperfect Information,” Rand
Journal of Economics, 15(3), 404–415.
Bennett, S. C. (2012): “Right to Be Forgotten: Reconciling EU and US Perspectives,
The,” Berkeley J. Int’l L., 30, 161.
Bernal, P. (2014): “The EU, the US and Right to be Forgotten,” in Reloading Data
Protection, pp. 61–77. Springer.
Daughety, A. F., and J. F. Reinganum (2014): “Revelation and Suppression of Private
Information in Settlement-Bargaining Models,” The University of Chicago Law Review,
pp. 83–108.
Koops, B.-J. (2011): “Forgetting footprints, shunning shadows: A critical analysis of
the’right to be forgotten’in big data practice,” .
McNealy, J. E. (2012): “The emerging conflict between newsworthiness and the right to
be forgotten,” Northern Kentucky Law Review, 39(2), 119–135.
O’Hara, K. (2012): “Can Semantic Web Technology Help Implement a Right to Be For-
gotten?,” Computers and Law, 22(6).
Rosen, J. (2012a): “Deciders: The Future of Privacy and Free Speech in the Age of Facebook
and Google, The,” Fordham L. Rev., 80, 1525.
(2012b): “The right to be forgotten,” Stanford law review online, 64, 88.
Walker, R. K. (2012): “Right to be Forgotten, The,” Hastings LJ, 64, 257.
Warren, S., and L. Brandeis (1890): “The Right to Privacy,” Harvard Law Review, 4(5).
38
Kim & Kim: The Right to be Forgotten
A Appendix A: Proofs
Proof of Lemma 1. When γ = 0, the left-hand-side of (3.1) is zero; the right-hand side is
p2CG > 0. The left-hand-side is increasing in γ with the slop S > 0. The slope of the right-
hand-side is p2S(gγγ + g). Because gγγ + g < 1, the positive LHS slope is strictly greater
than the RHS slope for any for any γ ∈ [0, γ] and for any p2 > 0. Therefore by the single
crossing property, there exists a unique γ > 0 that satisfies (3.1).
Proof of Lemma 2. Follows from the proof of Lemma 1 and the previous discussion in the
text.
Proof of Lemma 3. We want γG < γ to have some types of Google reject. Note that γG is
defined by (3.1), and is increasing in p2. Therefore, it suffices to have γG < γ at p2 = 1.
Define γ∗G such that it satisfies:
γ∗GS = g(h, γ∗G, S)γ∗GS + CG
Then γ∗G < γ is equivalent to:
CG < (1− g(h, γ∗G, S))︸ ︷︷ ︸(∗)
γS. (A.1)
Note that as γ∗G approaches γ, the term (∗) increases. Suppose that for γ∗G = 0, the con-
dition (A.1) holds. Then for any γ∗G > 0, this condition will hold. Therefore if CG <
(1− g(h, 0, S))γS, then γ∗G < γ, which implies γG < γ. Also note that by Lemma 1, γG > 0.
Therefore Google will neither accept no matter what her private information is nor reject not
matter what her private information is, assuming the petitioner’s case has merit (Assumption
1). Rather the petitioner’s claim will be accepted by Google whose type is sufficiently low
and rejected by Google for whom this is not the case.
Proof of Lemma 4. The petitioner’s expected payoff from litigation (if the claim is rejected)
depends on the posterior expectation of γ on the interval [γG, γ]. If γG increases, then γ(γG) =
E[γ|γ ≥ γG] increases (or the expected probability of winning in litigation, g(h, γ(γG), S),
decreases), and thus the expected value of litigation falls. Note that by construction, the
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Kim & Kim: The Right to be Forgotten
posterior expectation of γ concentrated on [γ∗, γ] makes P just indifferent between litigation
and give-up (i.e., (3.4) holds for γG = γ∗). For (i): When γG < γ∗, then P’s expected
payoff from litigation (when a posterior expectation of γ is concentrated on [γG, γ]) is greater
than that when it is concentrated on [γ∗, γ]. Therefore when γG < γ∗, the left-hand-side of
(3.4) becomes strictly positive, and so P must always litigate, i.e., p2 = 1. For (iii): When
γG > γ∗, p2 = 0 by the similar logic. For (ii): Lastly when γG = γ∗, P’s expected payoff
from litigation following rejection by the types γ ≥ γG = γ∗ is exactly the expected value
when the posterior is concentrated on [γ∗, γ]. By construction of γ∗, P is indifferent between
litigation and give-up after rejection by the types γ ≥ γG, and so P follows a randomized
strategy p2 ∈ [0, 1].
Proof of Proposition 1. Consider the subgame following the claim. Under Assumption 2,
the petitioner uses Bayes’ theorem to compute his posteriors on G’s type when the claim is
rejected.
(1) γG is defined by (3.1). We can easily see that γG is increasing in p2 and p2 ≤ 1, so that
γG ≤ γ∗G. Therefore if γ∗G < γ∗, then γG < γ∗. Given G’s cutoff strategy γG < γ∗, upon
rejection, P’s best-response strategy must be p2 = 1 by Lemma 4 (because litigation has a
higher expected payoff under the posterior concentrated on [γG, γ] than giving up). Against
P’s strategy p2 = 1, G’s best response is to use the cutoff strategy given by γG which equals
γ∗G when p2 = 1. Therefore G of types γ ≥ γ∗G reject the claim and otherwise accept, believing
that P will litigate with probability one. This in turn justifies P’s optimal strategy to be
p2 = 1. This is the only subgame-perfect Nash equilibrium after P’s claim.
(2) If γ∗G ≥ γ∗, then γG T γ∗ depends on P’s strategy p2. (i) First suppose that p2 = 0. Then
it must be γG = 0; i.e., any type of Google will reject the claim because they expect P to give
up for sure and thus earning zero instead of −γS by accepting the claim. Because γG = 0 <
γ∗, it must be p2 = 1 by Lemma 4, which is a contradiction. (That is, upon rejection by any
type, P learns nothing additional about G’s type, which implies that his posterior expectation
of γ equals his priors; however by Assumption 1, P will prefer to litigate than to give up and
so p2 = 1.) (ii) Now suppose that p2 = 1. Then γG = γ∗G (≥ γ∗). If γG > γ∗, then it must be
p2 = 0 also by Lemma 4, which is again a contradiction. (That is, if γG > γ∗ and p2 = 1, upon
rejection, P’s expected payoff from litigation when his posterior is on [γG, 1] is less than that
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when his posterior is on [γ∗, 1]; therefore it must be p2 = 0 contradicting p2 = 1.) Therefore
if p2 = 1, then it must be γG = γ∗G and γ∗G = γ∗. Note that p2 can be computed by plugging
in γ∗ in (3.1): p2 = γ∗Sg(h,γ∗,S)γ∗S+CG
=γ∗GS
g(h,γ∗G,S)γ∗GS+CG(by γ∗ = γ∗G) =
g(h,γ∗G,S)γ∗GS+CGg(h,γ∗G,S)γ∗GS+CG
(by
(3.5)), which confirms the petitioner’s strategy to litigate with probability one. (iii) Lastly
suppose that p2 ∈ (0, 1). Then it must be γG = γ∗ by Lemma 4. Given such cutoff strategy
of G, P is in fact just indifferent between litigation and give-up (See (3.4)), justifying that
P uses a randomized strategy p2 ∈ (0, 1). Now P’s strategy should confirm that G uses the
cutoff γ∗. Plugging γ∗ in (3.1), we have:
γ∗S = p2 [g(h, γ∗, S)γ∗S + CG] ,
which implies that p2 is uniquely determined by:
p2 =γ∗S
g(h, γ∗, S)γ∗S + CG. (A.2)
Therefore, believing P randomizes between litigation and give-up with probability given in
(A.2), G’s best response is to use the cutoff γG = γ∗. (Note that when γ∗ ≤ γ∗G, p2 < 1
implies γ∗S < g(h, γ∗, S)γ∗S+CG ≤ γ∗GS ↔ γ∗ < γ∗G.) Thus if γ∗G ≥ γ∗, G’s cutoff strategy
given by γG = γ∗ and p2 given by (A.2), where p2 = 1 iff γ∗ = γ∗G, is the only subgame-perfect
Nash equilibrium following the claim.
Proof of Proposition 2. Suppose that γ∗G < γ∗ for given h, S, CP , and CG, then γG = γ∗G
and p2 = 1 form a unique equilibrium in the subgame when p1 = 1, where P’s posterior
expectation of Google’s types is given by E(γ|γ ≥ γ∗G). Using backward induction, given the
unique subgame equilibrium, if c is such that
c ≤ F (γ∗G)h+ (1− F (γ∗G)) [g(h, γ(γ∗G), S)h− CP ] ,
then P will always prefer “claim” to “no claim.” Therefore, P’s strategy profile (p1, p2) =
(1, 1), G’s cutoff strategy with γG = γ∗G, and P’s posteriors E(γ|γ ≥ γ∗G) upon rejection form
a unique sequential equilibrium of this game. If c is larger than the right-hand-side of the
above inequality, then (p1, p2) = (0, 1), γG = γ∗G, and P’s posteriors E(γ|γ ≥ γ∗G) upon rejec-
41
Kim & Kim: The Right to be Forgotten
tion form a unique sequential equilibrium. That is, the specified strategies are sequentially
rational given the posterior beliefs f(γ)1−F (γG) and these beliefs are consistent with such strate-
gies. Sequential equilibrium implies subgame perfection; so if there were multiple sequential
equilibria, then there would also be multiple subgame perfect equilibria, contradicting the
uniqueness of Nash equilibrium in the subgame specified in Proposition 1. A similar argu-
ment proves that there is a unique sequential equilibrium in the case of γ∗G ≥ γ∗ for given h,
S, CP , and CG, except that now p1 = 1 if c ≤ F (γ∗)h and p = 0 if otherwise.
Proof of Proposition 3. As is evident from (4.1), there is a kink in (1 − F (γG)) at γ∗G = γ∗.
Let S∗ be a value of S such that γ∗G = γ∗ for given values of h, CP , and CG. Differentiation
of (4.1) yields:
dPr(“lawsuits”)
dS= (1− F (γG))
[∂p2
∂S+∂p2
∂γG
dγGdS
]︸ ︷︷ ︸
=dp2dS
−f(γG)p2dγGdS︸︷︷︸<0
.
First consider the case S < S∗ (or when γ∗G < γ∗). For given values of h, CP , and CG,
Assumption 2 can be rewritten in terms of S such that S > S for some S > 0 such that
(1− g(h, 0, S))γS = CG. These two conditions on S are in strict inequality and so continue
to hold for a small change in S. When S < S∗, p2 = 1 and γG = γ∗G; Then dp2dS = 0 and
total differentiation of (3.1) shows that γ∗G falls as S increases. So the derivative of (4.1) for
S ∈ (0, S∗) is −f(γ∗G)dγ∗GdS > 0. The probability of “lawsuits” thus unambiguously increases
with an increase in S when S < S∗. Next consider the case S ≥ S∗. Assumption 1 can
also be rewritten in terms of S of strict inequality such that S < S; and so for S ∈ [S∗, S),
the conditions still hold for a small increase in S. When S ≥ S∗, p2 = γ∗Sg(h,γ∗,S)γ∗S+CG
and
γG = γ∗, and so the derivative of (4.1) for S ∈ [S∗, S) is
− f(γ∗)dγ∗
dS+ (1− F (γ∗))
dp2
dS, (A.3)
where dp2dS < 0 and dγ∗
dS < 0. (Differentiation of (3.4) for γG = γ∗ with respect to S shows
that γ∗ falls as S increases. The derivative of the left-hand-side of (3.4) with respect to S is
negative holding γG = γ∗ fixed. Thus a decrease in the value of the left-hand-side of (3.4)
will decrease the borderline type γ∗. Also p2 monotonically decreases and converges to zero
42
Kim & Kim: The Right to be Forgotten
as S −→ S for S ≥ S∗.) Note that the right and left derivatives of Pr(“lawsuits”) differ at
S = S∗. At S = S∗, it is a special case where p2 = 1 and γG = γ∗ = γ∗G; the left derivative
evaluated at S = S∗ is then −f(γ∗)dγ∗
dS , which is greater than (A.3) at S = S∗. Now note
that limS→S(1− F (γ∗))p2 = 0, whereas (1− F (γ∗))p2 > 0 at S = S∗. Hence, the argmax of
Pr(“lawsuits”) ∈ [S∗, S). Define such argmax to be S; then (A.3)> 0 if S < S and (A.3)< 0
if S > S,42 which completes the proof. If we further impose the following condition, then the
probability of lawsuits achieves its unique maximum at the kink γ∗G = γ∗, i.e., S = S∗.
Assumption 3. −f(γ∗)dγ∗
dS |S=S∗ + (1− F (γ∗))dp2dS |S=S∗ < 0.
Assumption 3 implies that the right derivative of dPr(“lawsuits”)dS |S=S∗ < 0, and continues to
be negative for S > S∗.
Proof of Proposition 4. Inspection of (4.2) and Proposition 3 confirms this.
Proof of Propositions 5 and 6. Directly follow from the discussion in the text together with
Propositions 1 and 2. (We will add the technical details later.)
Proof of Proposition 7. Recall that the probability of lawsuits and the likelihood of broken-
links are given by (4.1) and (4.2), respectively. We can see that the left and right derivatives
differ at γ∗G = γ∗. We begin by the following lemma:
Lemma 5. An increase in the petitioner’s litigation cost, CP , has no effect on γ∗G, whereas
will decrease γ∗. On the other hand, an increase in Google’s litigation cost, CG, will increase
γ∗G, whereas has no effect on γ∗. Formally,
dγ∗GdCP
= 0,dγ∗
dCP< 0;
dγ∗GdCG
> 0,dγ∗
dCG= 0.
Proof of Lemma 5. γ∗G is defined by (3.5), in which we can easily see that γ∗G is not affected by
CP ; Differentiation of (3.5) with respect to CG shows thatdγ∗GdCG
> 0 holding other variables
fixed. On the other hand, γ∗, defined by (3.4) for γG = γ∗, is not affected by CG while
differentiation of (3.4) with respect to CP shows that dγ∗
dCP< 0.
42If we assume that f(γ)1−F (γ)
strictly increases in γ, then the second derivative of Pr(“lawsuits”) is negative
whenever (A.3)= 0. This ensures uniqueness of S. With a Uniform distribution F (·), this assumption is notnecessary. (Need to check if such condition is necessary for generic distribution.)
43
Kim & Kim: The Right to be Forgotten
(a) Lemma 5 implies that γ∗G < γ∗, Google’s optimal cutoff value γG = γ∗G increases with an
increase in Google’s litigation cost CG. Therefore, Pr(“lawsuits”) = (1−F (γ∗G)) falls with a
small increase in CG when γ < γ∗. On the other hand, when γ ≥ γ∗, Google’s optimal cutoff
value γ = γ∗ is not affect by a change in CG. Regardless, Pr(“lawsuits”) = (1 − F (γ∗G))p2
also falls with an increase in CG when γ∗G ≥ γ∗, due to the direct negative effect of CG on
p2 = γ∗Sg(h,γ∗,S)γ∗S+CG
. Thus an increase in CG always leads to a lower probability of lawsuits
with a kink at γ∗G = γ∗. For the likelihood of broken-links, when γ∗G < γ∗, it is given by
Pr(“broken links”) = F (γ∗G) + (1 − F (γ∗G))g(h, γ(γ∗G), S). As CG increases more types of
Google accept (i.e., the first term increases); while the probability of lawsuits, (1 − F (γ∗G))
and the expected probability of the petitioner winning in court, g(h, γ(γ∗G), S), both fall, and
so the multiplication of these two terms falls (i.e., the second term decreases). But a decrease
in the second term is dominated by an increase in the first term, because otherwise, for a
small ε > 0, it must be:
F (γ∗G + ε)− F (γ∗G) ≤ (1− F (γ∗G))g(h, γ(γ∗G), S)− (1− F (γ∗G + ε))g(h, γ(γ∗G + ε), S),
< g(h, γ(γ∗G), S)(F (γ∗G + ε)− F (γ∗G)),
where the inequality holds because g(h, γ(γ∗G), S) > g(h, γ(γ∗G + ε), S). This gives a contra-
diction because g(h, γ(γ∗G, S)) < 1. When γ∗G ≥ γ∗, the likelihood of broken-links is given
by Pr(“broken links”) = F (γ∗) + (1 − F (γ∗))p2g(h, γ(γ∗), S). An increase in CG does not
affect the interval of Google’s type who accept. This implies that P’s expected probability of
winning remains the same; however higher CG lowers P’s probability of choosing litigation,
and thus the probability of broken-links falls.
(b) Lemma 5 implies that when γ∗G < γ∗, γ∗G is not affected by CP . We can then easily ob-
serve that Pr(“lawsuits”) = (1− F (γ∗G)) remains constant by any small change in CP when
γ∗G < γ∗. Moreover, because γ∗G does not change, both the probability of rejection by Google
(and obviously the probability of acceptance) and P’s expected winning probability stay the
same. Thus Pr(“broken links”) = F (γ∗G) + (1− F (γ∗G))g(h, γ(γ∗G), S) also remains constant.
On the other hand, when γ∗G ≥ γ∗, γ∗ decreases with an increase in CP . So, the effect of an
increase in CP on Pr(“lawsuits”) = (1−F (γ∗))(
γ∗Sg(h,γ∗,S)γ∗S+CG
)seems not obvious because
we need to consider an indirect effect of CP on Pr(“lawsuits”) through γ∗. Let C∗P denote
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Kim & Kim: The Right to be Forgotten
the value of CP such that γ∗G = γ∗. Then for CP ∈ [C∗P , CP ) (or when γ∗G ≥ γ∗), we have:
dPr(“lawsuits”)
dCP=∂Pr(“lawsuits”)
∂γ∗dγ∗
dCP
= −f(γ∗)p2dγ∗
dCP+ (1− F (γ∗))
∂p2
∂γ∗dγ∗
dCP,
(A.4)
where the first term is positive because dγ∗
dCP< 0 by Lemma 5, whereas the second term is
negative because ∂p2∂γ∗ > 0. Note that the left and right derivatives differ at CP = C∗P . The left
derivative evaluated at CP = C∗P is zero (because p2 = 1 and γG = γ∗G = γ∗ at CP = C∗P );
whereas the right derivative evaluated at CP = C∗P is (1 − F (γ∗)) dp2dCP|CP=C∗P
< 0. The
derivative (A.4) remains negative for CP ∈ (C∗P , CP ) assuming f(γ)1−F (γ) strictly increases in γ.
Therefore, Pr(“lawsuits”) = (1−F (γ∗))p2 decreases in CP when γ∗G ≥ γ∗. For the likelihood
of broken-links in this case, we have Pr(“broken links”) = F (γ∗)+(1−F (γ∗))p2g(h, γ(γ∗), S),
where F (γ∗) decreases and 1−F (γ∗) increases by an increase in CP ; however any increase in
(1−F (γ∗)) is dominated by the decrease in the second term. So the likelihood of broken-links
also decrease in CP when γ∗G ≥ γ∗.
Proof of Proposition 8. First we prove that given the primitives that satisfy Assumptions 1
and 2 under both rules, γ∗ is lower under the British rule than under the American rule.
Given Google’s type γ, the petitioner’s expected payoff from litigation under the American
rule is
− (1− g(h, γ, S))h− c− CP , (A.5)
while under the British rule it is
− (1− g(h, γ, S))(h+ CP + CG)− c (A.6)
Suppose that two types of Google, γl and γh, such that γl < γh, are given. Let gl ≡ g(h, γl, S)
and gh ≡ g(h, γh, S). Obviously, gl > gh. Then the difference between the expected outcome
of litigating against the lower type γl and that against the higher type γh, under the American
rule, is
− (1− gl)h− c− CP − [−(1− gh)h− c− CP ] = h(gl − gh) > 0, (A.7)
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Kim & Kim: The Right to be Forgotten
whereas under the British rule it is
−(1−gl)(h+CP +CG)−c−[−(1−gh)(h+CP +CG)−c] = (h+CP +CG)(gl−gh) > 0. (A.8)
We can see that (A.8)>(A.7). In other words, the marginal benefit to the petitioner from
litigating against a lower type than against a higher type is greater under the British rule.
We can also see this by noting that the amount that depends on the trial’s outcome (win
or lose) is greater under the British rule. (The petitioner’s litigation cost CP under the
American rule can be seen as a fixed cost that incurs regardless of the trial’s outcome; on the
other hand under the British rule, the petitioner bears no litigation cost if he wins while pays
CP +CG if he loses.) This implies that there is more severe adverse selection problem under
the British rule, and thus the petitioner’s optimal cutoff type of Google, γ∗, is lower under
the British rule than under the American rule. The probability of lawsuits and the likelihood
of broken-links depend on γ∗G and whether γ∗G < γ∗ or γ∗G ≥ γ∗, given other parameters. We
now show that the effect on γ∗G of changing from the American rule to the British rule is
ambiguous. First recall that γ∗G under the American rule, denoted as γA satisfies
γAS = g(h, γA, S)γAS + CG, (A.9)
while γ∗G under the British rule, denoted as γB satisfies
γBS = g(h, γB, S)(γBS + CG + CP ). (A.10)
If the cutoff type γA under the American rule were to compare her loss γAS from accepting
and her expected court loss g(h, γA, S)(γAS + CG + CP ) from rejecting under the British
rule, then it depends on h, S, CP , and CG whether
g(h, γA, S)γAS + CG S g(h, γA, S)(γAS + CG + CP ),
↔ (1− g(h, γA, S))CG S g(h, γA, S)CP .(A.11)
If < in (A.11), then γB > γA; if > then γB < γA, and if =, then γB = γA. In particular,
when h, S, CP , and CG are such that g(h, 0, S)(CG + CP ) ≤ CG (the intercepts of the RHS
46
Kim & Kim: The Right to be Forgotten
when γ = 0 in (A.10) and (A.9) respectively), then γB < γA because gγ < 0 and so the slope
of the RHS of (A.10), gγ(γS + CG + CP ) + gS, is strictly less than the slope of the RHS
of (A.9), gγγS + gS. On the other hand, when g(h, 0, S)(CG + CP ) > CG, then it crucially
depends on (A.11). See Figure 7 for an illustration.
Figure 7: An illustration of γB ≷ γA
Then it follows that the probability of lawsuits and the likelihood of broken-links can either
rise, fall, or remain the same depending on the given parameter values, whether γB > γA,
and whether γB > γ∗ under the British rule.
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